Question

Explain why the modified duration measure only gives good estimates of price changes when the change in the market interest rate being considered is small.

Answer 1

The bond price has a convex relationship with rates, i.e,, the relationship is not linear. % change in price when yields fall is not the same as % change in price when yields rise. Modified duration assumes linear relationship. So when change is small, it captures good estimates. As for small schange, the convex relationship can be approximated as linear relationship. The difference between the actual relationship and linear relationship is very small for small change. However when the change is large, the difference between linear and convex relationship is huge and hence modified duration fails to capture.